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We have to find the distance the car has traveled after 3s. Actually this question came up in an important exam, and the answer was:

L=x(3)-x(0)

But I think this is the answer for displacement, not distance traveled by the car, because he is moving in a circular trajectory.

Suppose that the cars starts moving from point P and after three seconds it reaches point Q. By finding L=x(3)-x(0) do we find PQ following the curved line, or do we find the length of chord PQ?

enter image description here

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  • $\begingroup$ Although one can guess it - what is your exact question about that? $\endgroup$
    – ACuriousMind ♦
    Commented May 7, 2015 at 19:13
  • $\begingroup$ Hi Al.Ka. If you haven't already done so, please take a minute to read the definition of when to use the homework-and-exercises tag, and the Phys.SE policy for homework-like problems. $\endgroup$
    – Qmechanic ♦
    Commented May 7, 2015 at 19:51
  • $\begingroup$ @Qmechanic, sorry for removing your tag, but this isn't really a homework question! $\endgroup$
    – Al.Ka
    Commented May 7, 2015 at 19:59
  • $\begingroup$ I feel that this question isn't really about physics, but that the core seems to be about language and the use of it in physics. That said, "distance" is maybe less precise, but still (nearly) universally understood as the arclength of the curve. $\endgroup$
    – Martin
    Commented May 8, 2015 at 9:53

2 Answers 2

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What a strange question. Is $x(t)$ the distance measured along the track? Without defining $x$, there is nothing else to say. And if it is the distance, then it's the distance. Along the track. And the car is traveling along the track. So x is the distance. Which is what is asked.

I suggest you read http://www.physicsclassroom.com/class/1DKin/Lesson-1/Distance-and-Displacement

update

The "moving equation" in your title (I must admit I have not heard that term - could it be a translation of "equation of motion" from another language?) is

$$x(t) = 15 + 8t - t^2$$

Tabulating values for a few values of $t$:

t   x
0  15
1  22
2  27
3  30
4  31
5  30

you see that the distance covered is a parabola - and that the value of $x$ will go negative in just a few more seconds. All of this suggests that the value $x$ is indeed measured along the arc - if it was measured along the chord, it would have to be constrained to be between 0 and 40 (radius = 20m) and it most likely would have to have some oscillating component.

So I think that $x$ is the distance along the path, and $x(3)-x(0)$ is the distance covered between time $t=0$ and $t=3 s$. But unless somebody explicitly defines $x$, this is open to interpretation.

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  • $\begingroup$ I made my question more clear. I would appreciate an answer! $\endgroup$
    – Al.Ka
    Commented May 7, 2015 at 19:39
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    $\begingroup$ Yeah by "moving equation" I mean "equation of motion" (english is not my first language). Thank you for the answer! $\endgroup$
    – Al.Ka
    Commented May 7, 2015 at 20:03
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A trajectory or flight path is the path that a moving object follows through space as a function of time. The object might be a projectile or a satellite, for example. It thus includes the meaning of orbit—the path of a planet, an asteroid or a comet as it travels around a central mass. Read more here : http://en.wikipedia.org/wiki/Trajectory

I believe that the question is either wrong or incomplete because the trajectory given by $x(t) = 15+8t-t^2 $ is one dimensional , so how can the path (trajectory) be circular ?

Also, if the path is defined in just one dimension (x) , then the answer is definitely x(3) - x(0).

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